Questions and Answers Type: | MCQ (Multiple Choice Questions). |

Main Topic: | Quantitative Aptitude. |

Quantitative Aptitude Sub-topic: | Number System Aptitude Questions and Answers. |

Number of Questions: | 10 Questions with Solutions. |

- Find the LCM of 21, 28, and 32?
- 572
- 672
- 678
- 770

Answer: (b) 672

Solution:

Solution:

**Step(1):** Factorize the numbers into their prime factors.$$ 21 = 3 \times 7 = 3^{1} \times 7^{1} $$ $$ 28 = 2 \times 2 \times 7 = 2^{2} \times 7^{1} $$ $$ 32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^{5} $$ **Step(2):** Collect all the distinct factors with their maximum available power.$$ = 2^{5}, \ 3^{1}, \ 7^{1} $$ **Step(3):** Multiply the collected factors.$$ = 2^{5} \times 3^{1} \times 7^{1} $$ $$ = 32 \times 3 \times 7 = 672 $$

- Find the HCF of \(\frac{6}{7}\) and \(\frac{7}{8}\)?
- \(\frac{1}{56}\)
- \(\frac{1}{58}\)
- \(\frac{1}{62}\)
- \(\frac{1}{66}\)

Answer: (a) \(\frac{1}{56}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (6,7)}{LCM \ of \ (7,8)} $$ $$ = \frac{1}{56} $$

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (6,7)}{LCM \ of \ (7,8)} $$ $$ = \frac{1}{56} $$

- Find the HCF of 15, 25, 45?
- 2
- 3
- 4
- 5

Answer: (d) 5

Solution:**Step(1):** Factorize the numbers into their prime factors.$$ 15 = 3 \times 5 = 3^{1} \times 5^{1} $$ $$ 25 = 5 \times 5 = 5^{2} $$ $$ 45 = 3 \times 3 \times 5 = 3^{2} \times 5^{1} $$ **Step(2):** Collect all the common factors with their minimum available power.$$ = 5^{1} = 5 $$ Here, 5 is the highest positive number that can divide 15, 25, and 45 exactly.

Solution:

- Which one of the following is the LCM of \(\frac{15}{4}\), \(\frac{18}{5}\), and \(\frac{20}{7}\)?
- 120
- 150
- 180
- 220

Answer: (c) 180

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (15, 18, 20)}{HCF \ of \ (4, 5, 7)} $$ $$ = \frac{180}{1} = 180 $$

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (15, 18, 20)}{HCF \ of \ (4, 5, 7)} $$ $$ = \frac{180}{1} = 180 $$

- Find the HCF of 120, 150, 180?
- 10
- 20
- 30
- 60

Answer: (c) 30

Solution:**Step(1):** Factorize the numbers into their prime factors.$$ 120 = 2 \times 2 \times 2 \times 3 \times 5 $$ $$ = 2^{3} \times 3^{1} \times 5^{1} $$ $$ 150 = 2 \times 3 \times 5 \times 5 = 2^{1} \times 3^{1} \times 5^{2} $$ $$ 180 = 2 \times 2 \times 3 \times 3 \times 5 $$ $$ = 2^{2} \times 3^{2} \times 5^{1} $$ **Step(2):** Collect all the common factors with their minimum available power.$$ = 2^{1}, \ 3^{1}, \ and \ 5^{1} $$ **Step(3):** Multiply the collected factors.$$ = 2^{1} \times 3^{1} \times 5^{1} $$ $$ = 2 \times 3 \times 5 = 30 $$ Here, 30 is the highest positive number that can divide 120, 150, and 180 exactly.

Solution:

- Find the LCM of \(\frac{65}{20}\), \(\frac{75}{35}\), and \(\frac{80}{9}\)?
- 15600
- 15750
- 15820
- 15950

Answer: (a) 15600

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (65, 75, 80)}{HCF \ of \ (20, 35, 9)} $$ $$ = \frac{15600}{1} = 15600 $$

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (65, 75, 80)}{HCF \ of \ (20, 35, 9)} $$ $$ = \frac{15600}{1} = 15600 $$

- Which of the following is the HCF of 49, 64, and 99?
- 1
- 2
- 3
- 4

Answer: (a) 1

Solution:**Step(1):** Factorize the numbers into their prime factors.$$ 49 = 7 \times 7 = 7^{2} $$ $$ 64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{6} $$ $$ 99 = 3 \times 3 \times 11 = 3^{2} \times 11^{1} $$ There is no common number among the factors, so the HCF must be 1.

Solution:

- Which one of the following is the LCM of 7, 11, 13, and 17?
- 1
- 17017
- 7
- 65

Answer: (b) 17017

Solution:

Solution:

**Step(1):** Factorize the numbers into their prime factors.$$ 7 = 7^{1} $$ $$ 11 = 11^{1} $$ $$ 13 = 13^{1} $$ $$ 17 = 17^{1} $$**Step(2):** Collect all the distinct factors with their maximum available power.$$ = 7^{1}, \ 11^{1}, \ 13^{1}, \ and \ 17^{1} $$ **Step(3):** Multiply the collected factors.$$ = 7 \times 11 \times 13 \times 17 = 17017 $$

- Find the LCM of \(\frac{10}{9}\), \(\frac{12}{11}\), and 25?
- 2
- 150
- 300
- 600

Answer: (c) 300

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (10, 12, 25)}{HCF \ of \ (9, 11, 1)} $$ $$ = \frac{300}{1} = 300 $$

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (10, 12, 25)}{HCF \ of \ (9, 11, 1)} $$ $$ = \frac{300}{1} = 300 $$

- Find the HCF of 18, 24, and \(\frac{6}{5}\)?
- \(\frac{7}{5}\)
- \(\frac{4}{5}\)
- \(\frac{8}{5}\)
- \(\frac{6}{5}\)

Answer: (d) \(\frac{6}{5}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (18, 24, 6)}{LCM \ of \ (1, 1, 5)} $$ $$ = \frac{6}{5} $$

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)

$$ HCF = \frac{HCF \ of \ (18, 24, 6)}{LCM \ of \ (1, 1, 5)} $$ $$ = \frac{6}{5} $$

Lec 1: Introduction to Number System
Lec 2: Factors of Composite Number
Questions and Answers-1
Lec 3: Basic Remainder Theorem
Questions and Answers-2
Lec 4: Polynomial Remainder Theorem
Questions and Answers-3
Questions and Answers-4
Questions and Answers-5
Lec 5: LCM of Numbers
Questions and Answers-6
Lec 6: HCF of Numbers
Questions and Answers-7
Questions and Answers-8
Lec 7: Divisibility Rules of Numbers
Questions and Answers-9
Questions and Answers-10
Questions and Answers-11
Questions and Answers-12
Questions and Answers-13
Questions and Answers-14
Questions and Answers-15
Questions and Answers-16
Questions and Answers-17
Questions and Answers-18
Questions and Answers-19
Questions and Answers-20